The present invention relates to the testing and analysis of digital RF communications systems, and more particularly to a half-symbol constellation display that allows a user to easily recognize distortions in a modulated wireless communication signal.
There are various wireless communication systems that use different digital modulation formats. One such modulation format is the 3π/8-shifted 8PSK that is used in GSM/EDGE systems. For the transmission of a baseband signal that includes desired information, or symbols, a carrier signal is modulated by the baseband signal according to the modulation format, and filtered to limit the bandwidth. A discussion about such a transmission system is included in the Application Note 1298 provided by Agilent Technologies at http://cp.literature.agilent.com/litweb/pdf/5965-7160E.pdf. The characteristics of the bandwidth limiting filters used are different according to the particular modulation format. The GSM/EDGE system uses a Gaussian filter, for example, while other formats use a raised-cosine filter. The modulated carrier signal received by a receiver is down-converted to an intermediate frequency and then demodulated to produce I and Q component values for each symbol as well as a symbol clock. See Application Note 1314 provided by Agilent Technologies at http://cp.literature.agilent.com/litweb/pdf/5968-3579E.pdf.
Such a wireless communication system also requires signal test and measurement methods to assure quality of service. See Application Note 1313 provided by Agilent Technologies at http://cp.literature.agilent.com/litweb/pdf/9568-3578E.pdf. One such method is the use of a constellation diagram of the symbols on an IQ coordinate plane. Such a diagram or constellation display may indicate distortions due to noise or non-linearity of components in the system. FIG. 1 is a vector trajectory of symbols for the period of one burst length on an IQ coordinate plane according the 3π/8-shifted 8PSK modulation format, while FIG. 2 shows the symbols on a corresponding constellation display. The symbol locations are decided by sampling the I and Q components of a received signal according to the symbol clock.
FIG. 3 shows a relationship between an impulse response of an I or Q component and a symbol clock for the GSM/EDGE system. As mentioned above the GSM/EDGE system uses a Gaussian filter so the impulse response of the I or Q component of one symbol appears as a Gaussian curve. The symbol clock is phase locked to the peak of the impulse response, and the peak amplitudes of the impulse responses are sampled to decide the I or Q component values of the symbols, as shown at S2. In this case inter-symbol interference (ISI) exists at the points S1 and S3. The sampled I and Q component values of the symbols are displayed as shown in FIG. 2. If non-linearity and phase distortion exist, the symbol values shift radially and angularly respectively.
FIG. 4 shows another example of a relationship between an impulse response of an I or Q component signal and a symbol clock where the modulation format, such as 8PSK, uses a raised-cosine filter. This filter ideally does not cause ISI because there are no magnitudes except at the sample point S2. At all other symbol clocks the values are zero, as shown by points S0, S1, S3 and S4. Similar to the case for thef GSM/EDGE system, the sampled symbols may be presented in a constellation display for observing distortions included in the modulated signal.
The constellation display has some difficulty in observing distortions. For example FIG. 5 shows a constellation display of all possible symbols for the GSM/EDGE system that has more symbols than are shown in FIG. 2. FIG. 6 shows the same number of symbols as FIG. 5, but there are distortions due to non-linearity of the modulated signal. Even if more symbols are displayed, it may be difficult to clearly recognize the distortions at a glance because the symbols are sprinkled over the IQ coordinate plane.
U.S. Pat. No. 4,825,449 (McKissock) discloses a quantitative analysis of errors in a modulated signal which introduces the concept of error vectors. The error vector indicates the vector difference between an ideal and an actual vector for the symbols from the origin of the IQ coordinate plane. It provides an amount of the distortions of the signal under test. It may suggest that there is an error, but it is not clear what factor is the cause of the error. The user cannot recognize whether the error factor is due to noise or non-linearity in the system.
What is desired is an improved display for providing better observability of signal distortions in a modulated signal and the factors contributing thereto.